# Understanding Gas Laws: Quick Guide to Mastering Your Final Exam

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## Introduction

As you prepare for your final exam in chemistry or physics, understanding gas laws is crucial. This article will equip you with the knowledge to select and apply the correct gas law formulas, focusing primarily on the mathematical aspects necessary for solving exam problems. In this guide, we’ll cover various gas laws, the importance of unit conversions, and step-by-step problem-solving techniques. By the end, you’ll be ready to tackle any gas law question you encounter.

## The Importance of Gas Laws

Gas laws describe the relationships between pressure, volume, temperature, and the number of moles of a gas. Understanding these relationships is fundamental in predicting the behavior of gases in various situations. The primary gas laws include:

**Boyle's Law**: Relating pressure and volume at constant temperature.**Charles's Law**: Connecting volume and temperature at constant pressure.**Avogadro's Law**: Linking volume and the number of moles.**Ideal Gas Law**: unifying all aspects of gases into a single formula.

### Key Concepts to Remember

**Temperature must always be in Kelvin**: To convert Celsius to Kelvin, simply add 273.**Pressure conversions**: One atmosphere (atm) equals 760 torr or mmHg. Make sure to convert when necessary.**Understanding the variables**: Each law focuses on different variables, and recognizing which to use is crucial in solving problems efficiently.

## The Main Gas Laws and Their Applications

Each gas law presents unique conditions and relationships. Here’s a summary of the essential gas laws you need to know:

### Boyle's Law

**Formula**: ( P_1V_1 = P_2V_2 )

**Description**: At constant temperature, the pressure of a gas is inversely proportional to its volume.**Example**: If the pressure of a gas decreases, its volume increases, given a constant temperature.

### Charles's Law

**Formula**: ( \frac{V_1}{T_1} = \frac{V_2}{T_2} )

**Description**: At constant pressure, the volume of a gas is directly proportional to its absolute temperature.**Example**: Heating a gas increases its volume if the pressure remains constant, as demonstrated in hot air balloons.

### Avogadro's Law

**Formula**: ( \frac{V_1}{n_1} = \frac{V_2}{n_2} )

**Description**: The volume of a gas at constant temperature and pressure is directly proportional to the number of moles of the gas.**Example**: Doubling the number of moles of gas will double its volume, as long as temperature and pressure remain constant.

### Ideal Gas Law

**Formula**: ( PV = nRT )

**Description**: This law combines all the previous laws into one equation, incorporating pressure (P), volume (V), number of moles (n), the gas constant (R), and temperature (T).**Example**: Calculate the volume of a gas when the pressure, temperature, and moles are known.

## Choosing the Right Gas Law for Problems

When faced with a problem, follow these steps:

**Identify the given data**: Write down what you know and what you're trying to find.**Choose the appropriate formula**: Based on the variables available, select the gas law that fits the situation.**Convert units when necessary**: Always check your units for temperature and pressure to ensure they fit with the formula you are using.

### Example Problem Using Boyle's Law

#### Given:

- Initial Pressure (P1): 1 atm
- Initial Volume (V1): 550 mL
- Final Volume (V2): To be determined
- Final Pressure (P2): 2 atm

#### Steps:

**Apply Boyle's Law**: ( P_1V_1 = P_2V_2 )**Convert volume to liters**: 550 mL = 0.550 L**Rearrange for V2**: ( V2 = \frac{P_1V_1}{P_2} = \frac{1 atm * 0.550 L}{2 atm} = 0.275 L )

### Example Problem Using Charles's Law

#### Given:

- Initial Volume (V1): 106.0 L
- Initial Temperature (T1): 145 °C (418 K)
- Final Temperature (T2): 20 °C (293 K)

#### Steps:

**Convert temperatures to Kelvin**.**Apply Charles's Law**: ( \frac{V_1}{T_1} = \frac{V_2}{T_2} )**Rearrange to solve for V2**: Plug in values and calculate.

## Conclusion

Navigating gas laws can seem daunting, but with practice, you’ll find it quite manageable. Focus on remembering the relationships between pressure, volume, temperature, and moles, and you’ll be well prepared for your exam. Practice with various problems to reinforce these concepts, and you’ll gain confidence in selecting and applying the right gas law each time. Good luck!

after this video you'll finally understand which gas law you need to use and how to basically pick one every

single time you see a workout we're gonna start prepping for your final since that's your last exam

we're almost done I'm sure you're excited yes this is almost over so today we're gonna focus on gas laws the main

thing that we're gonna go over so I'm not going to necessarily go into the concepts I'm gonna just focus on the

math portion of this because that's really the majority of your exam it's all math based so I just want to teach

you all the different formulas as you already can see on the screen there are several that you will have to know and

then just knowing like which one to use from these word problems so first things first is super this is super important

before I even talk about all the different gas laws is this one key fact so little me saying importance yes this

is clearly important because for every single one of these formulas that includes temperature you have to make

sure that the units are going to be in Kelvin for every single gas law so if there isn't temperature of course in the

gas law don't worry about it but for the ones that do have you know temperature like all of these you always want to

make sure that your temperature is converted first to Kelvin or else it's going to automatically be wrong okay so

another thing is units so still knowing converting your different units I know I just mentioned temperature remembering

how to actually convert from Celsius to Kelvin so how we would do that is simply just whatever Celsius value we get we

would just add 273 and that will give us the new conversion in Kelvin the next thing is pressure so we will see that

maybe some answers might have like two different pressures and you're expected to at least convert it back down to one

of them they're either going to specify you know what pressure they what unit they want in pressure or you kinda have

to pick and just see if you want it both if you want both pressures to be in atmospheres or Torr or so on so this is

all the possibilities that I typically see for pressure this is kind of based on just the most common one so the most

equal to 760 millimeters mercury and the other ones I'd say aren't as common but just in case still something to know but

we'll go back to it we'll do several examples just want to cover all of our bases here since you're starting to

finally see gas laws now questions so far no no I've actually seen a little bit of this already in lab that's good

okay perfect I'm quiet okay and all of the different gas laws that you'll need to know so these are it's a the main

ones you probably will go over partial pressure as well dalton's law of partial pressures but

this is like the main ones that we start off with for gas laws so the first one is going to be Boyle's law and that's

really just talking about I don't kind of highlight here just it's basically just you know referring to pressure and

volume so we don't care about temperature or moles those are held constant we're specifically just looking

at pressure and volume next with Charles law that that's something a little bit different where we're now comparing

volume and temperature and then the next law is just comparing pressure and temperature Avogadro's law volume and

moles and then the combined gas law which I know tends to be pretty tricky because you're putting everything

together so you're comparing pressure volume and temperature and the last one that's a little bit different from the

other ones is the ideal gas law which compares basically everything so it has pressure volume and is our moles are is

a known gas constant that will be provided to you typically that's provided to you and then temperature so

I just say this is like the main ones that I would have memorized you know you have to have down to be able to answer

any of these questions so that being said I obviously don't expect you to know them right now so I do have a

little cheat sheet on the bottom just so you can pick from which one like what gas law we're actually using so how I

want you to start off these questions is just like we've done before where we have our given we write down our given

and and what we're finding and by doing so that's literally going to tell us what formula we should use so we are

said to have a 550 milliliter sample so right then and there I can see okay milliliters that is a unit for volume so

since I know my first volume okay I know that's B one is five hundred and fifty point zero milliliters next I'm gonna

keep going and say okay a sample of nitrogen gas is warmed from and it's giving me two different temperatures so

my first temperature is t1 so that's seventy-seven degrees Celsius and then my second temperature is 86 degree

Celsius so t2 so 86 degrees Celsius next it's telling me find the new volume if pressure remains constant so by them

even talking about pressure it's irrelevant because it's held constant that just means it doesn't do anything

there's no change we don't have to worry about it and they're not even talking about you know moles we don't have to

worry about that either the only thing that they're telling us is well we want to find our second volume so I'd go back

to my formulas and I'd see well what compares only volume and temperature well it has to be this one so volume and

temperature so I know I have to use that formula make sense yeah yeah I'd say the hardest part is just memorizing them all

it's just knowing which formula so it's I wouldn't say it's you know knowing which formula to use it's really just

remembering them all perfect so then the next thing we want to do before we just start plugging everything in is make

sure that we convert so let's convert both of these to Kelvin so if you were to plugged it in and you wouldn't have

converted anything it would been wrong so let's just simply add 273 to both of these temperatures and that's going to

convert Celsius to Kelvin so I'll do that now so 77 plus 273 this is going to give us 350 Kelvin and then the next one

86 plus 273 that'll be 359 Kelvin next thing I don't have to do anything with these milliliters I can just leave that

everything in at this point so on top I'll have v1 we said was 550 I'll just say milliliters for now and then

temperature we just changed this to 350 Kelvin next v2 is what we're solving for and then we've converted this one also

to Kelvin so what I'm going to start off doing is just dividing this and then I'll handle everything else so just

dividing these two values we're going to get one point five seven and I'm not going to round at all I around to the

very end I have seven one cool you move this over okay next step is to simply get v2 by itself so I'm going to remove

this denominator by multiplying it by both sides this would cancel and I now have to multiply these two together so

times 359 this is 5/6 4.14 then I'll round at the end just a little side note as to where the unit's go this would

have still have been milliliters divided by a Kelvin and then our Kelvin and our Kelvin cancel and that's why we're just

left with milliliters okay I was kind of wondering yeah and then I mean Plus you could also just think of it as like the

volume it has to be in milliliters it can't be in Kelvin or you know any sort of temperature unit then our final

answer so how many sig figs should we round it to I think four right cuz they all count so for this one yes but for

temperature there's only oh we're just looking to do a journey so we're looking at everything yeah

yeah because it's division yeah but yes it would have been too so I can actually round round down and say that

this is five 60 milliliters and that's our feature that's our second volume that's a cool since we know that this

zero does not count as significant only these two count right cool okay maybe not same sort of concept so

pretty much just changing the formulas I so I'm gonna start off and see that this is telling me what pressure and it tells

me what like what unit it wants for pressure so I know I'm looking for pressure and I specifically want this in

millimeters mercury next it's saying is required to compress this amount of volume so I know liters is a type of

volume so that's b11 96 liters and point zero and then of air at and then atmospheres is measured is actually

pressure so I know atmospheres pressure that's going to be my p1 actually it's going to have p2 and I'll explain how I

knew that into a cylinder whose temperatures volume is that actually it's not you know explain why so the

reason like this is also important to know like whether it be one you know p1 so on how I can just tell

is this keyword of all right I know that these two have to go together so those both have to either be 1 and 1 or 2 and

2 oh ok so it's you won them and that's p1 it correct all right so that's one I

need to actually pressure one atmosphere point zero zero atmospheres yeah and the next they're giving us a second volume

so I know that this is going to be my v2 and I'm looking for p2 and then luckily I don't have any temperature so I don't

have to convert anything I could either decide to convert this atmospheres to millimeters mercury right

now or I can do that the end really doesn't matter it's not gonna change the answer I'm gonna do at the end just to

make it easier so first I have to figure out what's the formula so what's the formula that is going to you know only

have volume and pressure well it's this first one right only volume and pressure that's all I'm worried about so I know

that I'm using this and if you were given all of them that would be so easy right yeah I wish and then from here I

just plug everything in so I know that p1 we said was one atmosphere B wine was 196 liters as equal to p2 which is what

we're solving for and v2 is twenty six point zero one actually put zero liters next I'm simply going to I'm actually

gonna do this on actually I can just really just moles by that I know it's just the same thing all right one times

196 is just gonna give us one ninety six point zero and I'll say this is liters times atmospheres since these two

combined and the next all I have to do is divide that 26 liters to both sides to find my answer okay and let's see

what that gives us so 196 divided by 26 p2 is equal to 7 point 5 3 8 4 and then remember that

leaders and leaders would cancel leaving us with atmospheres and this is p2 but we're not done yet we wanted our final

answer to be in millimeters mercury so I'm going to convert this and then I'll deal with sig figs and all that so this

goes back to our unit portion of this where one atmosphere is equal to 760 millimeters of mercury so I that's

something that you just had to remember okay so I'm gonna actually do this and just show that that's where I took

it from I know that one atmosphere is equal to 760 millimeters mercury that is my conversion factor and all convert

this so 7.5 3 8 4 atmospheres multiply this by 1 atmosphere on the bottom and 760 millimeters mercury on top

atmospheres atmospheres cancel and let's see what that gives us so this would give us 5 seven to nine point two three

just a little side note I didn't around this part like I'll actually write everything out that I then I put I had

in my calculator this was six one five three eight I don't want to round until the very very

end so that's what I actually put here so perfect and the next this is millimeters mercury last step is just to

figure out my sig figs so looking back since everything is multiplied what's our least amount of sig figs three yes

so I have to round to three sig figs so that being said we're gonna actually round up so if we see here we only want

three sig figs so I wouldn't just say 572 because that's different that changes the number entirely right from

5729 so I would just round this up to 30 so look at this next next number and I say okay threes next so this would be my

answer so this was PETA questions here no need to learn all of those yes that that's really it perfect do then the

next one so still the same sort of concept I'm still gonna start off with what's my given what's by finding and

then figure out the formula from you know what's given and what I'm finding so it's saying a gas balloon has a

volume so right there okay I know I have volume so I'm going to say I have V one is equal to 106 point 0 liters next that

amount when the temperature is so ok got on a new temperature so T 145 degrees Celsius next I see and the

pressure is so pressured this one's kind of nice literally tell me telling me what everything is so 740 point zero

millimeters mercury and it's asking what is what will its volume be at and now it gives me a new temperature a new

pressure so I know this is going to be a larger formula since I'm asked to find you know what's the new volume I'm gonna

solve for v2 they also give me another temperature here so t2 is 20 degrees Celsius and then a new pressure so p2 is

780 point zero millimeters mercury so since I have basically kind of like duplicates of everything right I have

two V volumes two temperatures two pressures I know that the only one that combines all of these is the combined

laws I think it's just yeah it's really just remembering all the formulas and knowing what to plug in where but other

than that it's not too bad and also knowing the converting units so units here the only thing we have to convert

so I'm simply going to add 273 to both temperatures so I can convert this so let's see what that gives us at 273 plus

45 to give us 318 Kelvin and then 20 plus well 273 that's gonna be 293 Kelvin perfect and next thing is really just

plug everything in yeah cool so I'm gonna start off with the first pressure all right it's fine that it's as long as

these two it'll know as long as these two are the same unit you don't have to convert anything but if this was and

let's say atmospheres then you would have to convert either you know this one to atmosphere like both of these top

so v1 was 106 point zero liters and then city t1 was our new value of 318 Kelvin and I'll set this equal anymore room to

p2 which was 780 point zero millimeters mercury v2 is what we're solving for and then t2 is 293 Kelvin okay so let's just

start off with doing all the math what I'm going to start off with is the left side so I'm going to multiply these two

together and then I'll divide by 3 18 so 740 times 106 so I'll just write what it actually gives me so that gives me 7 8 4

4 0 I'm gonna say this is millimeters mercury times leaders and then this is still divided by 318 Kelvin so now I'm

going to do this next part so I'm going to divide those two values and that'll be I'm not going to do any sort of

rounding to 246 points a lot of sixes and I'll say 7 2 so there we go this just repeats so the next I'm going to

now divide these two values just to make our lives easier so this is you know let me put the unit's as well this is still

millimeters mercury times liters / Kelvin since that's where I get it from I'll divide those two values so 780 /

millimeters mercury / Kelvin okay give me a second probably gonna remove some other stuff just to make our lives

is to simply just divide so that's a no - I'll divide this whole entire thing over so nothing too tricky here I'd say

it's pretty straightforward just knowing what formula tears yeah well so let me divide that and something we get Oh two

four six and that whole number okay so I get and I'm just gonna put it up here I get V two is ninety two point six five

eight and then I'm gonna see how many sig figs we need to round to so just looking at I'm gonna actually look at

everything that we multiplied here so just seeing what is the smallest amount well the smallest amount would have been

the Kelvin right so three sig figs would be our final answer so I'm gonna round up looking at that

five this would have been ninety two point seven and this would have been leaders okay some of this everything's

they didn't specify so if they would've asked like oh I want like like what is the volume in milliliters then we would

different I would say that this is a different formula and that's kind of why I have these gas constants I would all

explain how this works so once again what's given what are we finding well we're asked to calculate the volume so

our volume next they're giving us in liters so we actually this tells us right this tells us that it wants the

volume in liters next it says given two moles of h2o so now I'm giving them given moles so I know n is two moles

next it's telling me the temperature luckily that's already in Kelvin so our temperature and our pressure so we're

given temperature 300 Kelvin and then we're also given pressure so 1.25 Atmos okay well what's the only one that

allows us to you know basically combine everything and it's not like duplicates of up meaning we don't have to volume

two temperatures and so on well it's this last one the ideal gas law so I know that I'm going to use this an R is

actually it should be given to you and you're either gonna see it like this top one or this bottom one both of them are

the same so still the same thing one is just rounded the other one isn't so I'm gonna use I'm going to use the bottom

one that's kind of the main one that I will always use but it honestly doesn't matter so I'll put in pressure so P is

I realized one thing I wanted to mention so the units for all of this is totally fine because of the gas gas constants

units already so if you notice the units for our R it's already in liters atmospheres moles and Kelvin and this is

kind of like when we were talking about calorimetry with the specific heat capacity where all of the units have to

align or be the same as the specific heat capacity it's the same sort of concept here with the ideal gas law like

you want your moles to be in moles right we want that to be moles you want your pressure to be in atmospheres we always

want temperature to be in Kelvin and we're gonna want our volume to being leaders and that's why all of this is

totally fine however if we would have had let's say started with and I liked or four millimeters mercury you would

have had to add converted this to atmospheres just to match the gas constant does that mean okay

yes yeah same principle as before it's just uh yes yeah yeah exactly so cool two moles and then next or gas constant

so 0.0821 liters atmospheres divided by moles Kelvin sorry I used to had a student who would always think that this

right now I'd say it's very cute yeah whose high school student and every time you're like oh Mulk yep don't forget

about mulk loved it cool so we have everything we're solving for our volume and what I'm going to

start off with is the right side so just multiplying everything and seeing what that gives us

so 2 times everything else 2 1 so 4 at 9.2 6 will notice that the moles and moles will cancel Kelvin and Kelvin

cancel we're left with liters atmospheres and this continues I was hoping this down next step is to get

volume by itself so I'm going to divide both sides by that atmospheres so point 25 atmospheres this cancels our

atmospheres will cancel and we're gonna be left with just liters so this volume gives us thirty nine point four zero

eight liters last up is how many sig figs should we round to what do you think three try it again one yes I know

I know okay yeah and it's just because like what we did plug that all in right it's based on

whatever we plugged into the actual formula and since since this is multiplication division four sig figs we

look at the lowest amount so it is gonna be one so I'm actually going to round up so it's like I want this I'm gonna round

up so this is actually forty liters that's it okay cool awesome I fit I feel like this is easy right it's not too bad

yeah this is really nice compared to everything else that we've been doing so how do you

now that this makes sense this is this clicking with you let me know in the comment and of course if you need to go

re watch another portion of this video please do so remembering all of these gas laws is going to be really important